where \(v,w,z \in \mathcal {N}\) . Since the non-back tracking matrix \(B\)  is asymmetric, its eigenvalues are generally complex. Furthermore, a vast majority of eigenvalues lie within a circle in complex plain, with centre at the origin and with radius equal to the square root of the largest eigenvalue. Krzakala et al. [1]} hypothesized that the number of clusters in \(G\)  equals the number of real-valued eigenvalues outside the circle. Computing the eigenvalues of the non-back tracking matrix \(B\)  is of computational complexity \(O(L^{3})\) . However, the complexity can be reduced to \(O(N^{3})\) , as explained in [2]}. The non-back tracking matrix method is denoted as NBTM in Section .
